Question: Convert $813_9$ to base 3.
Solution: Since $9 = 3^2$, we can convert directly to base 3 by expanding each base 9 digit into two base 3 digits:   \begin{align*} 8_9 &= 22_3 \\ 1_9 &= 01_3 \\ 3_9 &= 10_3 \end{align*}  Putting the base 3 digit pairs together, we get $813_9 = \boxed{220110_3}$.